ORIGINAL ARTICLE

A New Method for Measuring the Oxygen Diffusion Constant andOxygen Consumption Rate of Arteriolar Walls
Nobuhiko Sasaki,1 Hirohisa Horinouchi, 3 Akira Ushiyama 2 and Haruyuki Minamitani 1
1 Graduate School of Science and Technology, Keio University, Tokyo, Japan

2 Department of Environmental Health, National Institute of Public Health, Saitama, Japan
3 Department of Surgery, School of Medicine, Keio University, Tokyo, Japan(Received for publication on March 29, 2011)(Revised for publication on July 6, 2011)(Accepted for publication on July 27, 2011)

Oxygen transport is believed to primarily occur via capillaries and depends on the oxygen tension
gradient between the vessels and tissues. As blood flows along branching arterioles, the O2 saturation
drops, indicating either consumption or diffusion. The blood flow rate, the O2 concentration gradient,and Krogh’s O2 diffusion constant (K) of the vessel wall are parameters affecting O2 delivery. We devised a method for evaluating K of arteriolar wall in vivo using phosphorescence quenching microscopy
to measure the partial pressure of oxygen in two areas almost simultaneously. The K value of arteriolar
wall (inner diameter, 63.5 ± 11.9 μm; wall thickness, 18.0 ± 1.2 μm) was found to be 6.0 ± 1.2 × 10 −11(cm2/s)(ml O2·cm−3 tissue·mmHg−1). The arteriolar wall O2 consumption rate (M) was 1.5 ± 0.1 (mlO2·100 cm−3 tissue·min−1), as calculated using Krogh’s diffusion equation. These results suggest that thearteriolar wall consumes a considerable proportion of the O2 that diffuses through it. (Keio J Med 61(2) : 57–65, June 2012)

Keywords: oxygen transportation, microcirculation, Krogh’s cylinder model, phosphorescencequenching method

Introduction

Recently, the drop in the partial pressure of oxygen (pO2)
across the blood–tissue interface6 and the drop in pO2 in
the arteriolar wall7 were reported to be greater than thosein the tissue outside the arteriole. These observations
indicate that either K of the arteriolar wall is extremely
low or that M of the arteriolar wall is extremely high.6
We therefore sought to produce an optical measurement
system to evaluate K and M of the arteriolar wall in vivo.
The arteriolar wall consists of endothelial cells, a basement membrane, vascular smooth muscle cells, mural
cells, and an interstitial matrix.8 For an arteriole with an
inner diameter of approximately 50 μm, the arteriolar
wall thickness is approximately 10–20 μm.7,9 Quantitative assessment necessitates that K and M of an arteriolar
wall be measured in vivo without vessel damage. Usinga special microscope system to precisely measure pO2,
we were able to calculate the values of K and M using the

Oxygen transport occurs by diffusion and is driven
by a concentration gradient. Krogh presented a cylindermodel to explain oxygen diffusion.1,2 In Krogh’s model,
oxygen is believed to be supplied to tissues by capillaries.
However, the oxygen saturation of hemoglobin in arteriolar blood decreases with increasing arteriolar branching.3 Several studies have reported that oxygen diffuses
through arterioles to tissues.4–6 Clarifying the oxygen
diffusion constant and consumption rate should improve
our understanding of this phenomenon. To elucidate oxygen consumption by, and diffusion through, arterioles,
Krogh’s oxygen diffusion constant (K) of the arteriolar
wall and the oxygen consumption rate (M) of the arteriolar wall must be determined; K is the product of the diffusion constant of oxygen (D) and oxygen solubility (α).2

Reprint requests to: Hirohisa Horinouchi MD, PhD, Department of Surgery, School of Medicine, Keio University, Shinanomachi 35, Shinjuku,
Tokyo 160-8582, Japan, E-mail: horinouc@a8.keio.jp, Secondary E-mail: horinouc@sc.itc.keio.ac.jp
Copyright © 2012 by The Keio Journal of Medicine
57

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Sasaki N, et al: Oxygen Diffusion and Consumption of Arteriolar Wall

60 mg/kg body weight) was used for anesthesia induction. Sevoflurane (1%) was administered through a mask
for maintenance of anesthesia. Animals were placed ona piezo stage, and the DSC was fixed with double-sided
tape. The surface temperature was monitored using athermocouple thermometer (AD5652; A&D, Tokyo, Japan).
Arteriolar wall
The arteriolar wall thickness5,7,9,14 was 10–25 μm forvessels with an inner diameter of 40–80 μm (Fig. 1;
27°C ±1°C tissue surface temperature in DSC; 400–500μm tissue thickness in DSC). All arteriolar walls wereobserved using the transmitted light of a halogen lamp
(KTS-150RSV; Kenko, Tokyo, Japan) because the excitation band of the oxygen measurement probe causes tissue photodamage. Photodamage caused by the influenceFig. 1 Arteriolar wall in a mouse dorsal skinfold chamber.
The arteriolar wall was clearly observed under white light. The of blue and green light was reduced using a wide-specinner diameter of this arteriole was 58.4 μm and the wall thickness trum halogen light for a short period. The wall thickness
was measured using a cooled CCD camera (DS-Qi1Mc;
was 18.6 μm. The scale bar indicates 50 μm.
Nikon, Tokyo, Japan) mounted on a microscope systemthat was assembled specifically for use in this study (Fig.
1; Newopto, Yokohama, Japan; The Optronics [Sankei],
10–12
equations presented in earlier reports.
Tokyo, Japan). The arteriole targeted in this study had awall thickness of approximately 18 μm, and this accomMaterials and Methods
modated the diameter of the laser beam (23 μm).
Animals
Experiments were performed using the mouse dorsal
skinfold chamber (DSC) model13 on 7- to 10-week-old
male BALB/c mice (Oriental Yeast, Tokyo, Japan) weighing 27–30 g. The mice were kept on a bed of pulp paper
in a ventilated, temperature-controlled (23°C ±1°C), specific pathogen-free environment with a 12-h light–darkcycle. They were given access to food and water ad libitum. All experimental protocols were reviewed by theCommittee on the Ethics of Animal Experiments at ouruniversity and were conducted in accordance with the
Guidelines for Animal Experiments issued by the Keio
University School of Medicine Experimental Animal
Center, and Law (No. 105) and Notification (No. 6) issued by the Japanese Government. The ethical guidelines
conformed to The American Physiological Society (APS)
guiding principles for the care and use of animals.
Mice were anesthetized for 1 h using ketamine (90 mg/
kg body weight) and xylazine (10 mg/kg body weight) for
DSC implantation. Detailed procedures of implantation
were described in an earlier report.13 When the DSC wasin place on the back of mice, the fascia was removed toobserve the subfascial microcirculation. Each mouse wasrested for at least 2 days to achieve stabilization of the microcirculation under DSC, consequently, all experiments
were conducted 2–6 days after DSC implantation.
At the time of measurement, ketamine–xylazine (7–ProbesFluorescein-labeled dextran (FITC-dextran; MW 2000
kDa, 10 mg/ml, 3 mL/kg body weight; Sigma-Aldrich,
St. Louis, MO, USA) was injected into the tail veins ofmice to observe the microcirculation and to measure thered blood cell (RBC) velocity in arterioles. After injecting FITC-dextran, Pd-meso-tetra (4-carboxyphenyl)
porphyrin (Pd-TCPP; 8.5 mg/ml, 3 mL/kg body weight;
Frontier Scientific, Logan, UT, USA) was injected as anoxygen probe. The Pd-TCPP was dissolved using a mixture (8:2) of 7.5% bovine serum albumin (Life Technologies, Carisbad, CA, USA) and phosphate buffer (pH 7.4;
Life Technologies, Carisbad, CA, USA). We measured
pO2 from 30–40 min after injecting Pd-TCPP,15 because
Pd-TCPP requires some time to spread from the vessels
to the tissues. During the waiting period, animals were
kept in a dark cage.
Microscope system for pO2 measurement
Pd-TCPP was excited by the second harmonic of a Qswitched neodymium-doped yttrium aluminium garnet pulse laser (wavelength, 532 nm; pulse width at half
maximum, 6 ns; irradiation energy, 200 nJ/pulse) throughthe objective lens (Fluor 40×/0.80 W; Nikon) of the mi-Keio J Med 2012; 61 (2): 57–65

59

exponential curve.16 Furthermore, pO2 was calculated bymeasuring τ according to the Stern–Volmer equation:5
I 0 τ0== 1 + τ 0 kq [C ]
I
τ

(1)

where C represents pO2, I is the light intensity, I0 is theinitial light intensity, τ is the phosphorescence lifetime,
τ0 is the phosphorescence lifetime at 0 mmHg O2, and kq
is the quenching coefficient (0.205 mmHg−1·s−1); τ0 was
0.658 ms (26.5°C) in our study following calibration.17
We constructed the microscope system to repeatedly
observe pO2 at two points almost simultaneously using
a piezo-driven stage (P517.2CL; ±5 nm repeatability, 250
Hz resonance frequency at 500 g loaded; PI Japan, Tokyo, Japan) and a controller (Figs. 2 and 3A; E-665 CR;
PI Japan). The stage vibrated horizontally within a designated distance, and motion was controlled by a personal
computer (Epson Direct Model 1127113; Epson Direct,
Fig. 2 Measurement system to determine K of the arteriolar wall.
Nagano, Japan).
The piezo-driven stage was used to measure pO in two areas us2

ing a microscope. The two measurement areas were located alternately under the laser beam using the piezo stage. We simultaneously measured pO2 in the two areas using Pd-TCPP and a
microscope. Laser parameters: 23-μm laser spot size, 200 nJ,
10 Hz, 6-ns half bandwidth. PMT, photomultiplier tube.

croscope (Fig. 2).16 The laser pulse recurrence frequency
was 10 Hz (when the oxygen diffusion constant was measured) or 2 Hz (when the oxygen consumption rate andother parameters were measured). The laser beam diameter at the focus position was 23 μm. At points other than
the focus position, the laser beam had a larger diameter.
Phosphorescence was weak in areas other than the focus
position. The photomultiplier tube (PMT; R1894; Hamamatsu Photonics, Hamamatsu, Japan) was unable to detect
the weak phosphorescence at points other than the focus
position. The reflected laser light and Pd-TCPP phosphorescence light were discriminated using a dichroic mirror(DM575; Nikon) and a long-pass filter (RG620; Nikon).
The phosphorescence intensity signal was transformed toa current signal by the PMT. Then, the current from the
PMT was transformed to a voltage signal by an analogto-digital converter (ADC; NR-2000; Keyence, Osaka,
Japan). The voltage signal from the ADC was sampled(sampling frequency, 200 kHz; 500 points sampled) using a personal computer (Fig. 2). Residual reflected laser
light, light leaked from the laser source, and tissue autofluorescence interfered with accurate measurement of
the phosphorescence signal. To eliminate these unwanted
effects, the phosphorescence signal was analyzed 50 μs
after initial detection of light signals.16 The phosphorescence lifetime (τ) was determined as the decay time to 1/eof the maximum phosphorescence intensity because thephosphorescence signal–intensity plot followed a single

Measurement model for K
The following assumptions were used to calculate K of
the arteriolar wall (Fig. 3A):
1. When mice inhaled pure oxygen, the increase in thepO2 of peri-arteriolar wall tissues was assumed to represent the increase in oxygen provided through the arteriolar wall alone, which resulted from the increase in
intra-arteriolar pO2.
2. Over a short period, the M values of the tissue andarteriolar wall were assumed to remain the same whenpure oxygen was inhaled.
3. The K values of blood (intra-arteriolar) and peri-arteriolar tissue were assumed to be higher than that of thearteriolar wall.
4. We chose a short longitudinal segment of the arteriole to reflect our assumption that oxygen diffusion occurs
in two dimensions in this model.
Following these assumptions, Krogh’s oxygen diffusion constant (K), the oxygen diffusion constant (D), andthe oxygen solubility of the arteriolar wall (α) were calculated using the following equations:2–4,10–12,18–21
K = Dα t(2)D=( Rc + x) 2 − Rc 2
4t

(3)

αt =

∆Pout ( Rc + x)
Vt ∆Pin Rc(4)

where D is the diffusion constant of oxygen through thearteriolar wall, αt is the oxygen solubility of the arteriolar

Sasaki N, et al: Oxygen Diffusion and Consumption of Arteriolar Wall

60

Fig. 3 Measurements required to calculate K and M of arteriolar wall.
(A) Changes in oxygen tension were required to calculate K. This representative curve shows the simultaneouschanges in pO2 at intra-arteriolar and peri-arteriolar locations before and after the mouse inhaled pure oxygen. Laser shots (10-Hz excitation) were emitted from a Q-switch laser oscillator: 50% of the shots were aimed at the intraarteriolar spot near the wall and 50% were aimed at the outer arteriolar peri-arteriolar spot. The piezo-driven stage
moved back and forth with a frequency of 10 Hz. In this representative schema, the arteriole has a wall thickness
and inner vessel diameter of 13.5 mm and 73.1 mm, respectively. Circle plots show intra-arteriolar pO2 and squareplots show outer peri-arteriolar pO2. Gray lines show moving averages of intra-arteriolar and extra-arteriolar pO2.
It took 5 s to observe an increase in intra-arteriolar pO2 after the mouse was switched to inhaling pure oxygen.
(B) Measurements of the oxygen consumption rate. The arteriole had a wall thickness and inner vessel diameter of
21.2 μm and 73.4 μm, respectively. The gray plot shows the pO2 at the laser-irradiated intra-arteriolar, wall center,and peri-arteriolar areas, representative of the pO2 of the inner edge, wall center, and outer edge of the arteriolar
wall, respectively (black plot). The analysis given in the text explains why the theoretical fitted line is the solid line
and not the dashed line. R is defined as the point of zero oxygen gradient. The gray zone represents the arteriolar
wall.

wall, Rc is the inner radius of arteriole, x is the thickness of the arteriolar wall, and t is the oxygen diffusion
time from the intra-arteriolar space to the exterior periarteriolar wall. In addition, ΔPin is the change in pO2 at
the inner edge of the arteriolar blood flow, and ΔPout isthe change in oxygen volume at the peri-arteriolar wall.
This volume change was derived from the change in pO2
at the inner edge of the arteriolar blood flow when the
animals were switched to inhale pure oxygen after breating normal room air, and the change in oxygen volume
was transformed from the change in pO2 at the exterior
peri-arteriolar wall using the published oxygen solubility
value for water (at 27°C and 1 atm).22 In addition, Vt is thearteriolar wall volume and Rc is the inner radius of thearteriole. On the basis of Brownian motion,20 Eq. 3 wasderived from two-dimensional diffusion and molecular
diffusion.19,23 The relation between arteriolar oxygen sol-ubility10,11 and oxygen tension at the peri-arteriolar area
and the inner-edge of the arteriolar wall are shown in
Eq. 4. In the equation, (Rc + x)/Rc, is a factor that adjusts
ΔPout, which might show a lower volume attributable totwo-dimensional diffusion.
Oxygen consumption rate model
The oxygen consumption rate of the arteriolar wall was
calculated from the observed value of the arteriolar wall
K, following the diffusion equations (Eqs. 5–8), as derived from Krogh’s cylinder model.1,2,24 In Krogh’s cylinder model, the cylinder comprises one capillary andthe theoretical cylinder tissue around the capillary outside the vessel wall. The cylinder tissue has an oxygen
concentration gradient that is dependent on the distancefrom the capillary wall. At the radius of the theoretical

Keio J Med 2012; 61 (2): 57–65

61

Table 1. Parameters of the arteriole
Parameter

Value

Mean red blood cell velocity
Arteriolar radius
Arteriolar wall thickness
Oxygen solubility of water (a)Difference of pO2 between intra- and periarteriolar regions
Intra-arteriolar pO2
Oxygen diffusion constant of arteriolar wall
(D)
Oxygen solubility of the arteriolar wall (at)Krogh’s O2 diffusion constant of arteriolar
wall (K)
Arteriolar wall O2 consumption rate (M)1.75 ± 0.81
31.8 ± 5.9
18.0 ± 1.2
0.028 *

mm/s
μm
μm
ml O2/ cm3 at 27°C, 760 mmHg

13.3 ± 2.6mmHg43.2 ± 6.5mmHg

2.0 ± 0.5 × 10 −6

cm 2 / s

3.1 ± 0.5 × 10 −5

ml O2 • cm−3 tissue • mmHg−1(cm 2/s)(ml O2 • cm−3 tissue •mmHg−1)(ml O2 • 100 cm−3 tissue • min−1)

6.0 ± 1.2 × 10 −11
1.5 ± 0.1

Values are mean ±SE.
*Ogi and Maruzen Co., Ltd., 2010 [16].

cylinder tissue, the oxygen concentration gradient is zero.
We regarded the arteriolar wall itself as comprising thecylinder tissue of Krogh’s model. We defined the boundary condition of the measured values of the intra-arteriole, wall center, and peri-arteriole. The pO2 value, as
retrieved from the spot where the laser beam contacted
the inner arteriolar wall, was assumed to be the pO2 of theinner edge of the arteriole (r = Rc). For the pO2 retrieved
from the wall center spot, the value was assumed as thepO2 of the wall center (r = Rc + x/2). The pO2 retrieved
from the spot where the laser beam contacted the outer
arteriolar wall was assumed to be the pO2 of the periarteriolar tissue (r = Rc + x) (Fig. 3B). The theoreticalcylinder tissue radius (R) of the arteriolar wall was calculated as the point where ∂Pt/∂r = 0 from curve fitting theoxygen diffusion gradient of the arteriolar wall (Fig. 3B).
∂P∂P 
 1 ∂ ∂Pt=
αt t K + ∂ 2t  − M
r
∂t
∂z 
 r ∂r ∂r

(5)

=
Pt P=
at r Rc
w

(6)

∂Pt
0=
=
at r R∂r(7)

Pt = Pw ( z ) +

M 2
MR 2
r
ln
r − Rc2 ) −
(
4K
2K
Rc

(8)

where Pt is the tissue pO2 (mmHg), Pw is the vessel wallpO2 (mmHg), r is the distance from the vessel center,
Rc is the vessel radius, K is the oxygen diffusion constant in units of (cm2/s)(ml O2·cm−3 tissue·mmHg−1), M
is the oxygen consumption rate in units of (ml O2·cm−3

tissue·s−1), αt is the oxygen solubility of the arteriolar wall
(ml O2·cm−3 tissue·mmHg−1), and R represents the cylinder tissue radius.
Results
Krogh’s oxygen diffusion constant of the arteriolar wall
We used seven mice for the experiments, and measurements were taken at three locations (i.e., within the arteriolar lumen close to the wall, the arteriolar wall, and in
the tissue just outside the arteriole) in the DSC for eachmouse. The K value of the arteriolar wall was calculated
from Eqs. 2–4. Parameters t, ΔPin, and ΔPout were measured. A representative experimental curve is shown in
Fig. 3A. The calculated K value of the arteriolar wall was
6.0 ± 1.2 × 10−11 (cm2/s)(ml O2·cm−3 tissue·mmHg−1) (N= 7), which is only around one-tenth of the K value formuscle described in previous reports (Table 1, 2). It took
about 5 s to observe an increase in intra-arteriolar pO2
after the mouse inhaled pure oxygen; it took another 2.0± 0.3 s before an increase in peri-arteriolar pO2 was detected. This time difference (2.0 ± 0.3 s) was defined as
the diffusion time (t). The pO2 in each region reached asteady state after 10–20 s from the start of the increaseof blood pO2. The thickness of the arteriolar wall (x) was
measured using a cooled CCD camera.
Oxygen consumption rate of the arteriolar wall
The data shown in Figure 3B gave a calculated M
value for the arteriolar wall of 1.5 ± 0.1 (ml O2·100 cm−3
tissue·min−1) (N = 7), which is similar to the M values ofmuscles described in previous reports (Table 2). Table 1
presents the arteriole parameters used in this experiment.

Sasaki N, et al: Oxygen Diffusion and Consumption of Arteriolar Wall

62

Table 2. Comparison of our results with published data
Author/year

AnimalArea (targeted tissue)

Bentley, 1993
Buerk, 1982

Hamster
RabbitRetractor muscle (at rest, in vivo)
Abdominal aorta, in vivo
Thoracic aorta, in vivo
Thoracic aorta, in vivo
Arteriole with anesthesia,
ex vivo
Arteriole without anesthesia,
ex vivo

Dog
Howard, 1966

Hamster

Human      K* (cm 2/s)(ml O2·cm−3 tissue ·mmHg−1)      9.38 × 10 −10      M** (mlO2·100 cm−3
tissue·min−1)      1.93      0.78      0.588      0.9      1.44      1.21

Mesentery with anesthesia, ex vivo      0.53

Pial artery, ex vivo      0.72

Navari, 1979

Cat

Paul, 1973

Cow

Pittman, 2005

Rat

Mesenteric vein,
ex vivo
Mesenterial arteriolar wall

Tsai, 1998

Rat

Mesenterial arteriolar wall, in vivo

This study

Mouse

Dorsal skin window chamberarteriolar wall, in vivo

The cylinder tissue radius (R) for the arteriole, which isthe distance between the arteriole center and the theoretical point of zero pO2 gradient of the arteriolar wall, isnecessary to calculate the oxygen consumption rate. The
calculated value for R was 56.3 ± 7.8 μm. To calculate
the theoretical point of zero pO2 gradient of the arteriolar
wall, we used a curve-fitting technique on the measured
pO2 values at the three locations. The three measurement
points were the intra-arteriolar, the wall center, and periarteriolar locations (Fig. 3B, gray plot) and these wereassumed to represent values taken from the inner edge,
wall center, and outer edge of the arteriolar wall (theoretical points; Fig. 3B, black plot), respectively. The calculated R value indicated that oxygen molecules that diffuse
through the arteriolar wall do not reach very far beyond
the outer edge of arteriole.
Discussion
Applicability of this method
We made several assumptions to facilitate our study ofthe K and M values of the arteriolar wall. Mahler measured the oxygen diffusion constant using a strip of muscle tissue.10 The tissue was placed
between two chambers; the upper chamber was insufflated with pure oxygen, and the oxygen concentration in
the lower chamber was measured. The times from insufflation of pure oxygen in the upper chamber to the time
when the oxygen concentration in the lower chamber

Polarography
Polarography
Polarography
Polarography
Cartesian divermethodCartesian divermethodCartesian divermethodCartesian divermethod      0.318

Polarography      15

Polarography
Phosphorescencequenching method
Phosphorescencequenching method      390      6.0 × 10 −11      Method      1.5

started to increase and when it reached a stable level were
measuredIn our method, the animals were switched to inhalationof pure oxygen after breathing normal room air. There
were several factors that influenced our measurements,
including the several seconds that it took before the increase in blood oxygen tension was observed, according
to the animal’s condition, and the difference between theoxygen diffusion constants of the intravascular space(blood) and extravascular space (interstitial tissue). For
these reasons, we could not use the same equations that
Mahler had used.
We selected a method for directly measuring the timerequired for an oxygen molecule to go from inside thearteriolar lumen to the outer edge of the arteriole, definedas the diffusion time. If the diffusion velocity of the oxygen molecule in the arteriolar wall was slow enough tomeasure, we could use the formula for diffusion of small
particles. This formula was first established by Einsteinin 1905 using the formula for Brownian movement ofmolecules in a medium.20 He gave the one-dimensional
solution as D = x2/2t. In this formula, D represents the
diffusion constant of the material, x is distance, and t is
time. Because diffusion from the arteriole was defined
two-dimensionally by Krogh, we used the two-dimensional formula D = x2/4t, where x represents the distancefrom the starting point of diffusion and t is time. Using
this formula, the oxygen diffusion constant of the arteriolar wall can be obtained when the thickness of the arteriolar wall and the time required for oxygen to reachKeio J Med 2012; 61 (2): 57–65

the outer arteriole wall is determined. We could measure
the time required as the time when we observed a changein oxygen concentration at the outer arteriolar wall edge.
Therefore, we used the formula for the diffusion constantgiven in Eq. 3.
Oxygen solubility (α) of the arteriolar wall was definedaccording to Mahler.10,11 Oxygen solubility of the arteriolar wall was determined using the change in oxygen
tension (volume) at the outer edge of the arteriole and theinner edge of arteriolar wall (Eq. 4). Although the oxygen
consumption rates of intra- and extra-arteriolar tissues
differed, the patterns of pO2 increase were similar (Fig.
3A). This phenomenon well supported our second measurement assumption that over a short period, the respective values of M (oxygen consumption rate) for the tissue
and arteriolar wall do not change.
The oxygen diffusion constant was measured using
phosphorescence-quenching analysis. Pd-TCPP molecules in the excited triplet state in the laser irradiation
area collided with oxygen molecules in the ground state.
Oxygen molecules that were in an excited singlet state
disappeared by reacting with nearby molecules. Consequently, pO2 recovered because of the diffusion of nearby
oxygen. However, to measure the oxygen diffusion constant, a laser must be used for the irradiation pulse interval before the oxygen diffusion phenomenon in tissue inorder to detect the velocity of oxygen movement. The inner and outer edges of the arteriolar wall were chosen as
the laser irradiation points. We predicted that the oxygen
diffusion constants of the intra-arteriolar bloodstream
and peri-arteriolar tissue areas would be higher thanthose of the arteriolar wall. The diffusion time of oxygenin the arteriolar wall was measurable; this fact suggeststhat the oxygen diffusion constant of the arteriolar wall
is lower than that in the surrounding tissue, indicatingthat our third assumption is valid. Furthermore, the pO2of laser-irradiated spots located beside the arteriolar wall
did not decrease during measurement. Each spot waslaser-excited with a 5-Hz frequency, which suggests thatthe oxygen consumption resulting from Pd-TCPP phosphorescence emission was very low and that the power
and time interval of the pulse laser irradiation were appropriate.
We used a 23-μm-diameter laser beam to measure oxygen tension by the phosphorescence-quenching method.
The laser beam diameter could have been smaller, but asmaller diameter would cause larger deviations becauseof the variety of cell types in the tissue. Pulsatile movement of the arteriolar wall might also contribute to such
fluctuations. Moreover, if we had used a smaller diameter
laser beam, to detect the appropriate strength of phosphorescence, a stronger laser power would have been necessary and this might have damaged the tissue. Therefore,
to detect stable average levels of tissue oxygen tension
semi-continuously without tissue damage, we used a
23-μm-diameter laser beam at the focus position.

63

Comparison of oxygen diffusion from the arteriolar
wall and oxygen consumption in the arteriolar wall
The amount of oxygen diffusion (QK) and oxygen consumption (QM) in the arteriolar wall were compared.
When a 100-μm length of arteriole is considered,6 theoxygen diffusion and oxygen consumption can be calculated from K and M values for the arteriolar wall using
Eqs. 9 and 10:
QK =⋅
K

∂pO2
⋅S
∂r

QM= M ⋅ Vt

(9)

(10)

where S is the inner surface area of the arteriolar wall,
Vt is the volume of the arteriolar wall, and ∂pO2/∂r is thepO2 gradient in the arteriolar wall.
The calculated QK was 1.4 × 10−10 (ml·s−1·100 μm−1 arteriole length), and QM was 1.2 × 10−10 (ml·s−1·100 μm−1
arteriole length) (Table 1). These data suggest that theoxygen that diffused from the lumen of the arteriole wasabsorbed into or consumed by the arteriolar wall. The
structure of the arteriolar wall is simpler than that of theaorta and arteries in general; the oxygen diffusion constant of the arteriolar wall is considered to be higher thanthat of either the aorta or artery walls. Smooth muscle
cells in the arteriolar wall require an abundant oxygen
supply. We used a laser-evoked phosphorescence decay
assay to evaluate the tissue oxygen tension. Because thepO2 gradient adjacent to the arteriolar wall was considered to be steep, the pO2 of the tissue obtained by our system might be lower than the true value. If this is the case,then the true M value might be lower than the calculated
value we obtained from the experimental data.
Oxygen balance (consumption and diffusion)
In the downstream direction, pO2 in arterioles has beenfound to decrease by 2–3% per 100 μm.28 We calculated
the oxygen loss (Q) for a 100 μm length of arteriole asfollows:
Q=
Vb ⋅∂Plose⋅ ( L・ v −1 ) −1
2∂z

(11)

where V b is the blood volume, ∂Plose/∂z is the oxygen loss
rate per 100 μm of arteriole, L is the length (a 100 μm inthis case), and v is the red blood cell velocity.
The pO2 loss rate per 100 μm of arteriole was calculated
as 4.5%±1.3% (N = 4). We also measured the RBC velocity and pO2 and calculated the oxygen balance. Calculations were conducted using the experimental data presented in Table 1; the mean RBC velocity for the wholearteriole was calculated based on the average velocity at

64

Sasaki N, et al: Oxygen Diffusion and Consumption of Arteriolar Wallthe center of the vessel (2.80 ± 1.31 mm/s) following the
Baker–Wayland model.24
The calculated oxygen loss, Q, of 1.8 ± 0.5 × 10−10(ml·s−1·100 μm−1 arteriole length) was very similar to theamount of oxygen diffusion, QK, [1.4 × 10−10(ml·s−1·100
μm−1 arteriole length)], demonstrating that the value of
K of the arteriolar wall was lower than that of the othertissues. Our study showed that the oxygen diffusion constant K of arteriolar wall was 6.0 ± 1.2 × 10 −11 [(cm2/s)(mlO2·cm−3 tissue·mmHg−1)], which was one-tenth the value
for hamster retractor muscle reported by Bentley.1 Muscle
is tissue that consumes oxygen to function, whereas arterioles comprise tissue conveying oxygen and nutrients. A
high oxygen diffusion constant in muscle tissue and low
oxygen diffusion constant in the arteriolar wall seems
rational for maintaining the oxygen balance. Previous
reports have presented various values for the oxygen consumption rate (Table 2). The values of M listed on Table
2 are close to 1 (ml O2·100 cm−3 tissue·min−1), except for
the value of 390 (ml O2·100 cm−3 tissue·min−1) reported
by Tsai et al.6 Thus, our results confirmed what many
investigators have reported over the past 40 years. The
high value reported by Pittman was calculated using thearrested flow method.26 We believe that they reported the
maximum value for wall consumption by assuming that
all of the oxygen disappeared from the arteriolar lumen,
thereby setting an upper limit on M. Differences in thevalues of various reports might result from differencesin the targeted tissues or measurement methods. Because
the arteriolar wall comprises various cell types (endothelium, smooth muscle cells, and pericytes) and matrices(basement membrane, collagen, and elastin), the results
show that the vessel wall functions partly as a barrier tooxygen and partly as a permeable membrane.

La Jolla, California) for discussions and valuable advice.
This study was supported in part by a Grant-in-Aid for
Scientific Research (H.H. No. C-21591824) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

Applicability of the results of this study
Because we measured the K of arteriolar wall, we wereable to assess the applicability of therapeutic approaches
that change the value of K. For example, if the experimentwere to be conducted in a hyperbaric oxygen chamber orafter administration of certain drugs that alter arteriolar
wall characteristics, the efficacy could be investigated. In
light of the oxygen cascade, the arteriole is inevitably inan upstream location. We would be able to increase theoxygen supply of capillaries and venules if we could reduce the value of arteriolar K or M, thereby producing an
oxygen-rich environment for peripheral tissues. Such arteriolar wall modifications might be useful for improving
the function of ischemic organs or altering tumor growth.
Acknowledgments
The authors are grateful to Prof. Marcos Intaglietta(Department of Bioengineering, University of California,

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